A classification of automorphic Lie algebras on complex tori

We classify the automorphic Lie algebras of equivariant maps from a complex torus to sl₂(C) . For each case, we compute a basis in a normal form. The automorphic Lie algebras correspond precisely to two disjoint families of Lie algebras parametrised by the modular curve of PSL₂(Z) , apart from four cases, which are all isomorphic to Onsager’s algebra.